THE BAROMETER FABLE

The following essay is frequently referred to, and often
reprinted in textbooks on writing. I recall it was also reprinted
in one of the Project Physics supplementary readers. Few people
recall its source, or its author.

As a bit of humor it is nicely constructed. As a parable with a
moral, it falls flat. What is the author's point, one wonders?
Is it an argument against a particular kind of pedantry in
teaching? Is it a demonstration that exam questions can be subject
to multiple interpretations? Is it an example of how a clever
student can find ingenious ways to answer a question?

Just what is the difference between exploring `the deep inner logic
of the subject' and teaching `the structure of the subject'.
Callandra doesn't make that difference clear, yet his student seems
not to like the first, but would rather have the second.

The title (which most people forget) is a clue. Medieval
scholastics were fond of debating such meaningless questions as
"How many angels can dance on the point of a pin," "Did Adam have
a navel," and "Do angels defecate." The emerging sciences replaced
such `scholarly' debates with experimentation and appeals to
observable fact. Callandra seems to be suggesting that "exploring
the deep inner logic of a subject in a pedantic way" is akin to the
empty arguments of scholasticism. He compares this to the `new
math', so much in the news in the 60s, which attempted to replace
rote memorization of math with a deeper understanding of the logic
and principles of mathematics, and he seems to be deriding that
effort also. So it still seems to me that we get no clear and
useful message from this essay.

On almost every level, this essay falls apart on critical analysis.
I wonder why it has become such a legend in the physics community?

-- Donald Simanek

Angels on a Pin

Some time ago I received a call from a colleague who asked if I
would be the referee on the grading of an examination question. He
was about to give a student a zero for his answer to a physics question,
while the student claimed he should receive a perfect score
and would if the system were not set up against the student: The
instructor and the student agreed to submit this to an impartial arbiter,
and I was selected.

I went to my colleague's office and read the examination question:
"Show how it is possible to determine the height of a tall building
with the aid of a barometer."

The student had answered: "Take a barometer to the top of the
building, attach a long rope to it, lower the barometer to the street
and then bring it up, measuring the length of the rope. The length
of the rope is the height of the building."

I pointed out that the student really had a strong case for full credit
since he had answered the question completely and correctly. On the
other hand, if full credit was given, it could well contribute to a high
grade for the student in his physics course. A high grade is supposed
to certify competence in physics, but the answer did not confirm this.
I suggested that the student have another try at answering the question
I was not surprised that my colleague agreed, but I was surprised that
the student did.

I gave the student six minutes to answer the question with the
warning that the answer should show some knowledge of physics. At
the end of five minutes, he had not written anything. I asked if he
wished to give up, but he said no. He had many answers to this problem;
he was just thinking of the best one. I excused myself for interrupting
him and asked him to please go on. In the next minute he
dashed off his answer which read:

"Take the barometer to the top of the building and lean over the
edge of the roof. Drop that barometer, timing its fall with a stopwatch.
Then using the formula S = ½at², calculate the height
of the building.

At this point I asked my colleague if he would give up. He
conceded, and I gave the student almost full credit.

In leaving my colleague's office, I recalled that the student had said
he had many other answers to the problem, so I asked him what they
were. "Oh yes," said the student. "There are a great many ways of
getting the height of a tall building with a barometer. For example, you
could take the barometer out on a sunny day and measure the height
of the barometer and the length of its shadow, and the length of the
shadow of the building and by the use of a simple proportion, determine
the height of the building."

"Fine," I asked. "And the others?"

"Yes," said the student. "There is a very basic measurement method
that you will like. In this method you take the barometer and begin
to walk up the stairs. As you climb the stairs, you mark off the length
of the barometer along the wall. You then count the number of marks,
and this will give you the height of the building in barometer units.
A very direct method."

"Of course, if you want a more sophisticated method, you can tie
the barometer to the end of a string, swing it as a pendulum, and
determine the value of 'g' at the street level and at the top of the
building. From the difference of the two values of `g' the height of the
building can be calculated."

Finally, he concluded, there are many other ways of solving the problem.
"Probably the best," he said, "is to take the barometer to the
basement and knock on the superintendent's door. When the superintendent
answers, you speak to him as follows: "Mr. Superintendent,
here I have a fine barometer. If you tell me the height of this building,
I will give you this barometer."

At this point I asked the student if he really did know the conventional
answer to this question. He admitted that he did, said that he
was fed up with high school and college instructors trying to teach
him how to think, using the "scientific method," and to explore the
deep inner logic of the subject in a pedantic way, as is often done
in the new mathematics, rather than teaching him the structure of the
subject. With this in mind, he decided to revive scholasticism as
an academic lark to challenge the Sputnik-panicked classrooms of America.